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Home/Chain Registry/Block #2,635,591

Block #2,635,591

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/29/2018, 7:19:10 AM Β· Difficulty 11.3265 Β· 4,194,998 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
57f0ef9fcc9919bdb28be014899eebd2164f1ec3aeef9c7cec5d9ffde260d895
View on Chainz β†—

Difficulty

11.326485

Transactions

2

Size

2.44 KB

Version

2

Bits

0b53947e

Nonce

268,615,400

Timestamp

4/29/2018, 7:19:10 AM

Confirmations

4,194,998

Merkle Root

b08f68f4af6d892f402a648a7028b89d0bf134f8ce7c3508a30d208c80547756
Transactions (2)
Coinbasee2e4f7059e982e…e650c081154bca
1 in β†’ 1 out7.8100 XPM110 B
AVjBsfQe…NYiz2VRN
384c4ee16f8330…4781ccd5f1442f
15 in β†’ 2 out3408.9210 XPM2.25 KB
ALrm27VJ…MP1rfFVHAVa5dYbR…j5uZYCvt
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.894 Γ— 10⁹⁢(97-digit number)
18944002715036933342…98024236617297059840
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
1.894 Γ— 10⁹⁢(97-digit number)
18944002715036933342…98024236617297059839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.788 Γ— 10⁹⁢(97-digit number)
37888005430073866684…96048473234594119679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.577 Γ— 10⁹⁢(97-digit number)
75776010860147733368…92096946469188239359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.515 Γ— 10⁹⁷(98-digit number)
15155202172029546673…84193892938376478719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.031 Γ— 10⁹⁷(98-digit number)
30310404344059093347…68387785876752957439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.062 Γ— 10⁹⁷(98-digit number)
60620808688118186695…36775571753505914879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.212 Γ— 10⁹⁸(99-digit number)
12124161737623637339…73551143507011829759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.424 Γ— 10⁹⁸(99-digit number)
24248323475247274678…47102287014023659519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.849 Γ— 10⁹⁸(99-digit number)
48496646950494549356…94204574028047319039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.699 Γ— 10⁹⁸(99-digit number)
96993293900989098712…88409148056094638079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.939 Γ— 10⁹⁹(100-digit number)
19398658780197819742…76818296112189276159
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 2635591

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 57f0ef9fcc9919bdb28be014899eebd2164f1ec3aeef9c7cec5d9ffde260d895

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,635,591 on Chainz β†—
Circulating Supply:57,888,843 XPMΒ·at block #6,830,588 Β· updates every 60s
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